Synchronization Conditions of a Mixed Kuramoto Ensemble in Attractive and Repulsive Couplings

Ha, Seung‐Yeal; Kim, Dohyun; Lee, Jaeseung; Noh, Se Eun

doi:10.1007/s00332-021-09699-0

Cited by 7 publications

(6 citation statements)

References 42 publications

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“…( 16) Then in this case, we directly set t 0 = 0. Therefore, from ( 15), (16), and Lemma 3.2, we derive the upper bound of D 0 (θ) on [t 0 , +∞) as below…”

Section: Lemma 32 Let {θmentioning

confidence: 99%

“…The rigorous mathematical treatment of synchronization phenomena was started by two pioneers Winfree [43] and Kuramoto [27,28] several decades ago, who introduced different types of first-order systems of ordinary differential equations to describe the synchronous behaviors. These models contain rich emergent behaviors such as synchronization, partially phase-lcoking and nonlinear stability, etc., and have been extensively studied in both theoretical and numerical level [1,3,5,11,14,15,16,17,19,26,32,39].…”

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confidence: 99%

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Emergence of synchronization in Kuramoto model with frustration under general network topology

Zhu¹

2022

NHM

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<p style='text-indent:20px;'>In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data are confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [<xref ref-type="bibr" rid="b25">25</xref>] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and an invariant set confined in quarter circle after some finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.</p>

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“…( 16) Then in this case, we directly set t 0 = 0. Therefore, from ( 15), (16), and Lemma 3.2, we derive the upper bound of D 0 (θ) on [t 0 , +∞) as below…”

Section: Lemma 32 Let {θmentioning

confidence: 99%

mentioning

confidence: 99%

Emergence of synchronization in Kuramoto model with frustration under general network topology

Zhu¹

2022

NHM

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show abstract

“…The terminology synchronization represents the phenomena in which coupled oscillators adjust their rhythms through weak interaction [1,29], and Kuramoto model is a classical model to study the emergence of synchronization. The emergent dynamics of the Kuramoto model has been extensively studied in literature [2,3,5,13,14,16,17,18,19,23,26,30]. In our work, to fix the idea, we consider a digraph G = (V, E) consisting of a finite set V = {1, .…”

Section: Introductionmentioning

confidence: 99%

Emergence of synchronization in Kuramoto model with general digraph

Zhang¹,

Zhu²

2021

Preprint

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In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in order to capture the dissipation structure on a general network, we apply the node decomposition criteria in [22] to yield a hierarchical structure, which leads to the hypo-coercivity. This drives the phase diameter into a small region after finite time in a large coupling regime, and the uniform boundedness of the diameter eventually leads to the emergence of exponentially fast synchronization.

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Section: Introductionmentioning

confidence: 99%

Emergence of synchronization in Kuramoto model with frustration under general network topology

Zhu¹

2021

Preprint

View full text Add to dashboard Cite

In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data is confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [25] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and a small invariant set after finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.

show abstract

Synchronization Conditions of a Mixed Kuramoto Ensemble in Attractive and Repulsive Couplings

Cited by 7 publications

References 42 publications

Emergence of synchronization in Kuramoto model with frustration under general network topology

Emergence of synchronization in Kuramoto model with frustration under general network topology

Emergence of synchronization in Kuramoto model with general digraph

Emergence of synchronization in Kuramoto model with frustration under general network topology

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